1、Ch.13 Energy III:Conservation of energyCh.13 Energy III:Conservation of energyCh.13 Energy III:Conservation of energyIn this chapter:we consider systems of particles for which the energy can be changed by the work done by external forces(系统外的力)and nonconservative forces.ffiiUKUK+=+Law of conservatio
2、n of mechanical energy:“In a system in which only conservative forces do work,the total mechanical energy remains constant”Ch.13 Energy III:Conservation of energy13-1 Work done on a system by external forcesPositive external work done by the environment on the system carries energy into the system,t
3、hereby increasing its total energy;vice versa.The external work represents a transfer of energy between the system and the environment.extsyssysWUK=+(13-1)Ch.13 Energy III:Conservation of energyLet us consider a block of mass mattached to a vertical spring near the Earths surface.1.system=block.Here
4、 the spring force and gravity are external forces;there are no internal forceswithin the system and thus no potential energy.Using Eq(13-1),gravspringWWK+=EarthFig 13-2An exampleCh.13 Energy III:Conservation of energy2.System=block+spring.The spring is within the system.3.System=block+Earth.Here gra
5、vity is an internal Force.4.System=block+spring+Earth.The spring force and gravity are both internal to the system,sogravspringWUK=+springgravWUK=+0=+gravspringUUKCh.13 Energy III:Conservation of energy13-2 Internal energy(内能)in a system of particles1.Consider an ice skater.She starts at rest and th
6、en extend her arm to push herself away from the railing at the edge of a skating rink（溜冰场）.icerailingUse work-energy relationship to analyze:extWUK=+The system chosen only include the skaterMgNF0=UCh.13 Energy III:Conservation of energyWF=0;WN+MG=0;Wext=00=K?in disagreement with our observation that
7、 she accelerates away from the railing.Where does the skaters kinetic energy come from?Ch.13 Energy III:Conservation of energyFor a system of particles,it can store one kind of energy called“internal energy”.The problem comes from:The skater can not be regarded as amass point,but a system of particl
8、es.extWUK=+It is the internal energy that becomes the skaters kinetic energy.extWEUK=+int(13-2)Ch.13 Energy III:Conservation of energy2.Whats the nature of“internal energy”?Sum of the kinetic energy associated with random motions of the atoms and the potential energyassociated with the forces betwee
9、n the atoms.intintintUKE+=Ch.13 Energy III:Conservation of energySample problem13-1A baseball of mass m=0.143kg falls from h=443mwith ,and its .0=ivJmghUUUif621)(0=JmvKf1260212=0int=+EUK0=extFsmvf/42=Find the change in the internal energy of the ball and the surrounding air.Solution:system=ball+air+
10、Earth.JKUE495int=Ch.13 Energy III:Conservation of energy*13-3 Frictional work 1.Consider a block sliding across a horizontaltable and eventually coming to rest due to the frictional force.For the system=block+table,no external force does any work on the system.Applying Eq(13-2)(13-4)As the decreases
11、,there is a corresponding increase in internal energy of the system.0int=+EKKfvextWEUK=+intCh.13 Energy III:Conservation of energy2.If the block is pulled by a string and moves with constant velocity.f=T?fsWf=fvTFor the system=block+tableTtableblockWE=+int,extWEUK=+intWTis responsible for increasing
12、 the internal energy(temperature)of the blockand table.Ch.13 Energy III:Conservation of energyFor the system=block fTblockWWE+=int,fWTs+=fWfs+=(f=T)If Wf=-fs,.It is in disagreement with observation.0int,=blockEfsWfSo,it must be:is correct only if the object can be treated as a particle(不考虑内部结构时).fsW
13、f=Ch.13 Energy III:Conservation of energySample problem 13-2 A 4.5 kg block is thrust up a incline with an initial speed vof 5.0m/s.It is found to travel a distance d=1.5 mup the plane as its speed gradually decreases to zero.How much internal energy does the system of block+plane+Earthgain in this
14、process due to friction?30Solution:System=block+plane+Earth,ignore the kinetic energy changes of the Earth.)(intKUE+=extWEUK=+intJmgdmghUUUif3330sin0)(=JmvKKKif562102=JKUE23)(int=+=Ch.13 Energy III:Conservation of energy13-4 Conservative of energy in a system of particlesWe illustrate these principl
15、es by considering block-springcombination shown in Fig 13-4.the spring is initially compressed and then released.(a)(b)(c)Fig 13-4fWfWsWfF,extintsys,syssysWEUK=+(13-2)Ch.13 Energy III:Conservation of energy(1)system=block.(13-8)fsWWEK+=+int0=Ubecause the spring is not part of the system.(2)System=bl
16、ock+springfWEKU=+int(13-9)(3)System=block+spring+table0int=+EKU(13-10)The frictional force is a nonconservative dissipative force.The loss in mechanical energy being compensated by an equivalent gain in the internal energy.Ch.13 Energy III:Conservation of energyIn Fig 13-5,even though the railing exerts a force on the skater,it does no work.13-5 Equation of CM energyFrom Eq(7-16),(),we suppose the center of mass moves through a small displacement.Multiplying on both sides by this ,we obtain=cmex